Computation of Nash Equilibria of Attack and Defense Games on Networks

TL;DR

This paper demonstrates that Nash equilibria in attack and defense network games can be computed efficiently in polynomial time, introducing an algorithm with O(n^4) complexity.

Contribution

It proves polynomial-time computability of Nash equilibria in attack-defense network games and presents a new O(n^4) algorithm.

Findings

Nash equilibrium can be computed in polynomial time.

Proposed algorithm runs in O(n^4) time.

Theoretical proof of polynomial-time solvability.

Abstract

We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the network. We propose an algorithm that runs in O(n4) time with respect to the number of nodes of the network, n.